To set up the stage for such conclusions, in Section 2 we consider the 1+1+2 split of the Kerr metric similar to that of [1]}, [2]}, early developed for non-rotating black holes. Note that the standard 1+3 separation of coordinates has been employed to rotating black holes as in framework of the Membrane Paradigm and in the fluid/gravity correspondence as well (see, e.g., [3]}, [4]}, [5]}, [6]}, [7]}, [8]}, [9]}, [10]}). The explicit 1+1+2 decomposition of metric for rotating black holes a là Parikh-Wilczek has not been considered in literature, to the extent we know.
